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 A094567 Associated with alternating row sums of array in A094566. 4
 1, 4, 30, 203, 1394, 9552, 65473, 448756, 3075822, 21081995, 144498146, 990405024, 6788337025, 46527954148, 318907342014, 2185823439947, 14981856737618, 102687173723376, 703828359326017, 4824111341558740, 33064951031585166, 226630545879537419 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (6,6,-1). FORMULA a(n) = F(4n+1) - a(n-1) for n >= 1, with a(0) = 1. a(n) = (Fib(4n+3) + (-1)^n)/3. - Ralf Stephan, Dec 04 2004 a(n) = 6*a(n-1)+6*a(n-2)-a(n-3), with a(0)=1, a(1)=4, a(2)=30. - Harvey P. Dale, Jul 13 2011 G.f.: (1-2*x)/(1-6*x-6*x^2+x^3). - Harvey P. Dale, Jul 13 2011 a(n) = (-1)^n*sum((-1)^k*Fibonacci(4*k+1), k=0..n). - Gary Detlefs, Jan 22 2013 a(n) = (2^(-n)*(5*(-2)^n+(7-3*sqrt(5))^n*(5-2*sqrt(5))+(5+2*sqrt(5))*(7+3*sqrt(5))^n))/15. - Colin Barker, Mar 05 2016 EXAMPLE Obtain 4,30,203 from a(0)=1 and Fibonacci numbers 1,5,34,233: 4=5-1, 30=34-4, 203=233-30. MATHEMATICA RecurrenceTable[{a[0]==1, a[n]==Fibonacci[4n+1]-a[n-1]}, a[n], {n, 30}] (* or *) LinearRecurrence[{6, 6, -1}, {1, 4, 30}, 31] (* Harvey P. Dale, Jul 13 2011 *) PROG (PARI) Vec(-(2*x-1)/((x+1)*(x^2-7*x+1)) + O(x^100)) \\ Colin Barker, Nov 19 2014 (PARI) vector(30, n, n--; (fibonacci(4*n+3) + (-1)^n)/3) \\ Michel Marcus, Nov 19 2014 CROSSREFS Cf. A000045, A094566. Sequence in context: A268218 A272493 A246151 * A134093 A007905 A084976 Adjacent sequences: A094564 A094565 A094566 * A094568 A094569 A094570 KEYWORD nonn,easy AUTHOR Clark Kimberling, May 12 2004 EXTENSIONS More terms from Harvey P. Dale, Jul 13 2011 STATUS approved

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Last modified August 10 15:18 EDT 2024. Contains 375056 sequences. (Running on oeis4.)